Multiply the following complex numbers: $({-3+2i}) \cdot ({-4})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3+2i}) \cdot ({-4}) = $ $ ({-3} \cdot {-4}) + ({-3} \cdot {0}i) + ({2}i \cdot {-4}) + ({2}i \cdot {0}i) $ Then simplify the terms: $ (12) + (0i) + (-8i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 12 + (0 - 8)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 12 + (0 - 8)i - 0 $ The result is simplified: $ (12 - 0) + (-8i) = 12-8i $